xtife: Interactive Fixed Effects Estimator for Balanced Panel Data

xtife provides a pure base-R implementation of the Interactive Fixed Effects (IFE) panel estimator of Bai (2009) with full analytical standard errors, asymptotic bias correction, and information-criterion-based factor number selection. No external dependencies beyond base R are required. For a comprehensive review about interactive fixed effect, please refer to Ditzen, J., & Karavias, Y. (2025).

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The Model

Standard two-way fixed effects (TWFE) assumes unobserved heterogeneity enters additively. IFE generalises this by allowing unobserved confounders to interact across units and time:

$$y_{it} = \alpha_i + \xi_t + X_{it}'\beta + \lambda_i'F_t + u_{it}$$

where $F_t \in \mathbb{R}^r$ are common factors and $\lambda_i \in \mathbb{R}^r$ are unit-specific loadings. Setting $r = 0$ reduces the model to standard TWFE.

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Features

Feature	Details
Estimator	Bai (2009) SVD-based alternating projections
Standard errors	Homoskedastic, HC1 robust, cluster-robust by unit
Bias correction	Bai (2009) static; Moon & Weidner (2017) dynamic
Factor selection	IC1, IC2, IC3 (Bai & Ng 2002); IC(BIC), PC (Bai 2009)
Dynamic extension	Predetermined regressors (Moon & Weidner 2017)
Dependencies	Base R only (stats)
Panel type	Balanced panels

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Installation

# From CRAN (once available)
install.packages("xtife")

# Development version from GitHub
# install.packages("remotes")
remotes::install_github("Rickchen0910/xtife")

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Quick Start

library(xtife)
data(cigar)   # 46 US states x 30 years cigarette panel (Baltagi 1995)

# Fit IFE with r = 2 factors, two-way FE, cluster-robust SE
fit <- ife(sales ~ price, data = cigar,
           index  = c("state", "year"),
           r      = 2,
           force  = "two-way",
           se     = "cluster")
print(fit)

Interactive Fixed Effects (Bai 2009, Econometrica)
-------------------------------------------------------
        Estimate Std.Error  t.value   Pr(>|t|) CI.lower CI.upper
price    -0.5242    0.0802  -6.5360     0.0000  -0.6814  -0.3670

Converged: TRUE  (10 iterations)
N = 46  T = 30  r = 2  force = two-way  se = cluster

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Standard Error Types

fit_std <- ife(sales ~ price, data = cigar,
               index = c("state", "year"), r = 2, se = "standard")
fit_rob <- ife(sales ~ price, data = cigar,
               index = c("state", "year"), r = 2, se = "robust")
fit_cl  <- ife(sales ~ price, data = cigar,
               index = c("state", "year"), r = 2, se = "cluster")

se =	Assumption	Typical use
"standard"	Homoskedasticity	Benchmark
"robust"	HC1 sandwich	Heteroskedasticity across cells
"cluster"	Cluster-robust by unit	Serial correlation within units

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Factor Number Selection

sel <- ife_select_r(sales ~ price, data = cigar,
                    index = c("state", "year"),
                    r_max = 6,
                    force = "two-way")

Prints a table of IC1, IC2, IC3 (Bai & Ng 2002), IC(BIC), and PC (Bai 2009) criteria for each candidate $r$. The recommended criterion for panels with $\min(N, T) < 60$ is IC(BIC).

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Asymptotic Bias Correction

# Static bias correction (Bai 2009)
fit_bc <- ife(sales ~ price, data = cigar,
              index = c("state", "year"), r = 2,
              bias_corr = TRUE)

# Dynamic bias correction (Moon & Weidner 2017)
# Use when regressors include lagged dependent variables
fit_dyn <- ife(sales ~ price, data = cigar,
               index = c("state", "year"), r = 2,
               method    = "dynamic",
               bias_corr = TRUE,
               M1        = 1L)

For the cigar panel ($N = 46$, $T = 30$, $T/N \approx 0.65$):

Estimator	Price coefficient
IFE (r = 2)	−0.5242
IFE + Bai (2009) bias correction	−0.5309
IFE dynamic + Moon & Weidner (2017) bias correction	−0.5343

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Comparison with TWFE

Setting r = 0 recovers the standard two-way FE estimator, identical to lm() with unit and time dummies at machine precision:

fit0 <- ife(sales ~ price, data = cigar,
            index = c("state", "year"), r = 0)
# Equivalent to plm(..., model = "within", effect = "twoways")

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Function Reference

Function	Description
ife()	Fit IFE model; returns coefficients, SEs, factors, loadings
print.ife()	Print formatted coefficient table and model info
ife_select_r()	Fit IFE for r = 0, …, r_max and compare information criteria

Key ife() arguments

Argument	Default	Description
formula	—	outcome ~ covariate1 + ...
data	—	Long-format data.frame
index	—	c("unit_col", "time_col")
r	1	Number of interactive factors
force	"two-way"	Additive FE: "none", "unit", "time", "two-way"
se	"standard"	SE type: "standard", "robust", "cluster"
bias_corr	FALSE	Apply analytical bias correction
method	"static"	"static" (Bai 2009) or "dynamic" (Moon & Weidner 2017)
M1	1L	Lag bandwidth for dynamic B1 bias term

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About

Author

Binzhi Chen (University of Essex)

Email: Binzhi.Chen9@gmail.com

Web: https://sites.google.com/view/binzhichen/home

Citation

Please cite as follows:

Chen, B. (2026). xtife: Interactive Fixed Effects Estimator for Balanced Panel Data. R package version 0.1.0. https://github.com/Rickchen0910/xtife.

Or

@Manual{xtife, title = {{xtife}: Interactive Fixed Effects Estimator for Balanced Panel Data}, author = {Binzhi Chen}, year = {2026}, note = {R package version 0.1.0}, url = {https://github.com/Rickchen0910/xtife}, }

References

Bai, J. (2009). Panel data models with interactive fixed effects. Econometrica, 77(4), 1229–1279. doi:10.3982/ECTA6135

Bai, J. and Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica, 70(1), 191–221. doi:10.1111/1468-0262.00273

Baltagi, B.H. (1995). Econometric Analysis of Panel Data. Wiley.

Ditzen, J., & Karavias, Y. (2025). Interactive, Grouped and Non-separable Fixed Effects: A Practitioner's Guide to the New Panel Data Econometrics. arXiv preprint arXiv:2507.19099. https://doi.org/10.48550/arXiv.2507.19099

Moon, H.R. and Weidner, M. (2017). Dynamic linear panel regression models with interactive fixed effects. Econometric Theory, 33, 158–195. doi:10.1017/S0266466615000328

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License

GPL-2 | GPL-3 © 2026 Binzhi Chen